Envlron. Sei. Technol. 1083, 17, 20-26
Aerosol Filtration by a Cocurrent Moving Granular Bed: Penetration Theory Thomas W. Kalinowski*~tand Davld Leith Department of Environmental Health Sciences, Harvard School of Public Health, Boston, Massachusetts 02 115
A penetration model for aerosol filtration by a cocurrent moving bed of granules has been developed. The model incorporates straight-through penetration and reentrainment of previously collected dust, the latter due to granule motion, both mechanisms having been found significant in experiments. The model, an extension of classical clean granular bed theory, utilizes the familiar concept of a single-granule coefficient for collection and proposes a similar coefficient for reentrainment. Reentrainment was found in experiments to be a function of particle size and other factors such as gas velocity, granule velocity, and the extent of intergranular dust deposit. The single-granule reentrainment coefficient for moving granules, nR, was found to depend upon the product of intergranular dust deposit and the square root of dust-particle diameter (Kd,1/2) for particle diameters between 0.16 and 5.5 pm.
Introduction Granular bed filters are of interest for collection of particles from hot gas streams in advanced power-generation systems such as combined cycle coal gasification or pressurized fluidized bed coal combustion (1-7). A recent review of granular bed filtration theory and experiments is provided by Yung et al. (8). A common feature of practical granular-bed filters is bed motion for granule cleaning and recharge and for control of pressure drop. Most previous experiments and theory concerned stationary clean beds. Theoretical prediction of particle collection by granules commonly involves solving equations of motion for particle trajectories accounting for collection forces and the flow field around an isolated collector. Common assumptions include (1) low dust concentration in the gas, (2) no dust accumulation on the collectors, and (3) complete retention of all particles that contact a collector (9). These studies are useful to explain results from clean-bed experiments but have not been extended to more practical, loaded-bed cases. Recent theoretical studies to model loaded granular beds by Payatakes et al. (10, 11) and Goren (12) consider enhanced particle collection by previously captured particles as well as reentrainment of collected particles. These authors show that hydrodynamic factors affecting particle collection by already deposited particles or by dendrites near the surface of a granule are complex. Factors affecting reentrainment are also poorly understood. However, reentrainment in moving granular bed filtration experiments significantly affects overall bed efficiency (7, 13). A penetration model for a moving granular bed filter must account for reentrainment related to granular motion. This paper presents a theoretical treatment of particle penetration through a cocurrent moving granular bed fiiter (CMGBF). The present model explicitly accounts for reeritrainment as a particle penetration mechanism, in addition to penetration due to failure to collect, Le., penetration straight through. Data are provided that characterize the factors affecting reentrainment. Penetration Model A previous study (13)of CMGBF performance showed that some dust penetrates straight through and some 'To whom correspondence should be addressed at Kennedy/ Jenks Engineers, 657 Howard Street, San Francisco, CA 94105. 20
Environ. Sci. Technol., Vol. 17, No. 1, 1983
captured dust is reentrained due to granule motion. Furthermore, penetrating dust from these two sources had different size distributions. This paper considers these two separate penetration mechanisms and discusses a model that is an extension of the classical clean granular bed filtration model, to which it reduces when reentrainment is negligible. Mass Balance on the Aerosol. In the CMGBF shown in Figure 1, clean granules and dusty gas are added continuously at the bed top, then pass downward cocurrently, and exit at the bed bottom. A unique feature of the CMGBF is the controlled formation of an intergranular dust deposit to ehance filtration of submicron particles. A mass balance on the aerosol in the differential volume, A dZ, is rate in = rate out + accumulation QgC = Qg(C + dC) + E - R (1) where E = collection rate and R = reentrainment rate. Solution of eq 1requires expressions for the differential collection and reentrainment rates. Particle Collection*Rate. Consider particle collection analogous to classical clean-bed theory except that the single-granule collection coefficient, vG, accounts for the effect of dust adhering to the granule as well as for the granule itself. The collection rate, E , can be expressed as the product of the cross-sectional area swept clean by these collectors and the particle flux through the differential volume:
In eq 2, the fraction of the differential volume occupied by granules is indicated by 1minus the clean bed porosity, E,. The porosity, e, in the flux expression is the effective porosity accounting for reduced voidage due to the intergranular dust deposit. The superficial gas velocity, Vg, divided by the effective porosity, E , is the interstitial gas velocity. Equation 2 is developed by assuming particle collection in the dirty bed remains related to the granules, that is, complete "cake filtration" does not occur here as it would if all void space were entirely dust filled. Particle Reentrainment Rate. Consider a particle reentrainment rate, R , based on removal of dust already collected and adhering to the granule surface. The expression for the mass of collected dust in the differential volume is m = spppA dZ (3) where pp = dust particle density (kg/m3) and sp= solidity of dust deposit (volume of dust/volume of bed, dimensionless). Next define a gas parcel as the gas volume equivalent to the volume of a single granule. The number of gas parcels per second passing each granule is given by ? ? d ~ ~v/g4 N=(4) ? ? d ~ ~ /e 6
A dimensionless single-granule reentrainment coefficient, rlR, will now be defined as the fraction of all dust adhering to a single granule that is reentrained from that granule
0013-936X/83/0917-0020$01 .SO10
0 1982 American Chemical Society
I
i
a continuous mode with a steady-state dust deposit. It cannot be used if the inlet concentration varies significantly or is zero. Equation 10 does not describe transient responses such as initial deposit buildup or deposit deterioration when the dust feed stops. Equation 10, which is general, can be applied to particle collection in any cocurrent moving granular bed, whether collected particles reentrain or not. If no reentrainment occurs (qR 0), eq 10 reduces to the classical granular bed penetration equation (4, 14, 15):
-
dZ
For a demonstration of the effect of reentrainment on bed performance, consider the situation when the bed is very deep, i.e., z a;in this case
-
Pt,,, Figure 1. Schematlc dlagram of CMGBF.
by a single gas parcel passing it. The reentrainment rate in the differential volume is the product of eq 3,4, and the single-granule reentrainment coefficient:
Substituting eq 2 and 5 into eq 1gives an expression for the mass balance on the aerosol:
Before eq 6 can be integrated across the depth, Z, of the bed, an expression for sp in terms of dust concentration, C, is required. Mass Balance at Steady State. The CMGBF is designed for continuous operation, and at steady state all dust that enters the bed must leave in the aerosol stream or on the granules. With the assumption that dust entering on the granules is negligible, a mass balance at steady state on total dust in the aerosol and on the granules yields QgCi =
QgC
+ Q G S ~ P ~ -/ (eo) ~
(7)
Solving eq 7 for spproduces sp
= Qg(Ci - C)(1 - ~ , ) / ( Q G P ~ )
=& !
"/[+ 21
T G QG
Note: Z positive in downward direction
(8)
where Ci = entering aerosol concentration (kg/m3). Substituting eq 8 into eq 6 yields
Integration of eq 9 yields
This is the theoretical expression for steady-state particle collection and reentrainment in a cocurrent moving granular bed filter operating under the conditions of a continuous dust feed rate at constant concentration. These assumptions are appropriate for the CMGBF operating in
1
(12)
-
Even if particles are collected efficiently, i.e., qG 1, significant penetration may occur if reentrainment is important, ?& > 0.
Discussion of Theory Effective Porosity. In the integration of eq 9, it was assumed that the effective porosity, E , is independent of bed depth. This approximation is valid when the steady-state dust deposit is established near the bed surface so that it does not vary appreciably throughout the bed depth, For the experimental operating conditions described below, pressure-drop data at intermediate bed depths indicated that a stable deposit was formed within 2 or 3 cm of the bed surface in 13-cm deep beds. One of the unique features of the CMGBF is its ability to function as a "graded media" filter, i.e., larger dust particles are collected on clean granules at the bed surface while smaller particles are collected within the bed pores by an increasingly dense dust deposit. An optimal CMGBF design may be one in which graded media filtration is achieved throughout the bed depth. However, some depth of a uniform dust deposit appears desirable to collect submicron particles that might otherwise penetrate, but an excessively deep bed may result only in pressure drop and reentrainment penalties. As demonstrated previously (13), the CMGBF can provide high collection efficiency with a shallow bed; however, particle reentrainment must be controlled to maintain low overall penetration. Fpr the steady-state dust deposits achieved in our experiments, the solidity of the dust, sp,was less than 0.04, i.e., more than 90% of the clean-bed void space remained open. However, the effective porosity, e, may be estimated by (13) e = eo - sppp/pbp where sp = solidity of dust deposit (dimensionless), pq = dust particle density (kg/m3), and pbp = loose bulk density of dust (kg/m3). Equation 13 reflects the fact that, due to higher resistance to airflow through the dust deposit, essentially all gas flow occurs through the dust-free void space between granules. Equation 13 can be used to estimate the effective porosity, E , utilized in eq 10. Factors Affecting Reentrainment. Although many theories are available to describe clean-granule efficiency, no adequate theories are presently available to predict the single-dirty-granule efficiency, TG, or to predict the single-granule reentrainment coefficient, ?)R. As a first apEnviron. Scl. Technol., Vol. 17, No. 1, 1983 21
proximation, a lower bound for efficiency of the conditioned granule, Do, might be calculated frqn theory for clean, unconditioned granules. Reentrainment should depend upon the ratio of separation force to adhesion force for particle-to-granule and particle-to-particle interactions. A review of the literature suggests that these forces, for other than the most simple configurations, are poorly understood and cannot be predicted accurately. Adhesion forces include van der Waals, electrostatic, and surface tension capillary forces. As humidity increases, capillary forces become more singificant and electrostatic charges leak away. In general, adhesive forces increase with particle size (16). Corn (17)gave expressions for van der Waals forces and capillary forces acting between a spherical particle and a surface that show that these forces are directly proportional to particle diameter. Separation forces should be related to air drag and mechanical shear, the latter caused by granule slippage. For small particles in the Stokes region suspended in air, drag force is proportional to particle diameter. Thus, the ratio of separation force to adhesion force, were only simple Stokes drag to apply, would be independent of particle size. However, because particles are attached to granules or other particles, the flow fields around attached particles are complex, as a velocity gradient exists near a granule’s surface. Fuchs (18) indicated that two attached particles in a velocity gradient experience a separation force related to the second power of particle diameter. Goren and ONeill (19) determined the drag force on a particle attached to a granule (dp 5 according to Delaplaine (21). Delaplaine (21) found, in experiments with glass beads or sand flowing in tubes with tube-to-granule diameter ratios greater than 20, that approximately 80% of the bed cross-sectional area in the central core flowed in a cohesive, rodlike manner, and shear occurred in the outer 20% of the flowing bed. Toyama (24)observed similar flow regions in a glass-front rectangular bed by using layers of different colored granules and reported that the shear region at the wall was 4-8 granule diameters thick. Grossman (23) showed calculated shear stress profiles at various bed depths and radical positions that indicate maximum shear stress at the wall and rapidly decreasing shear stress away from the wall, particularly for shallow beds ( Z / D < 2). According to Grossman (23), shear stress at the wall increases with the wall friction coefficient, p’, and decreases with the internal friction coefficient, p. The coefficient of friction at the wall, p‘, was not found to be a function of bed velocity or granule size in Delaplaine’s experiments with dry systems and no interstitial fluid flow. Brandt and Johnson (22) found a slight increase, about 25%, in p’ over a bed velocity range of 0-5 mm/s (30 cm/min) for 20-40 mesh ion-exchange resin in a lucite tube with cocurrent water flow, the p’ was independent of the relative fluid velocity through the bed. These studies suggest that within the CMGBF there exist axial and radial distributions of compressive and shear forces acting on the granules and adhering dust. It is likely that the presence of dust on the granules alters the friction Coefficients p and p’ compared to clean granule friction coefficients. Within the plug-flow portion of the bed, the dust layer on a granule may be stable and perhaps compacted. However, near the wall, shear stresses become large and cause granule slippage. If, at the onset of slippage, the shear forces overcome particle adhesion forces, particles will separate and may be resuspended by interstitial gas flow. On this basis, the reentrainment coefficient, VR, should increase in conjunction with factors that increase shear stress within the bed such as bed depth ( Z / D < 5), granular bulk density, column diameter, and pressure drop from cocurrent fluid flow. The maximum shear stresses that can develop will depend on the friction coefficients, p and p’, which in turn are influenced by the presence of the dust and must be determined empirically. Temperature Effects. The single-granule collection coefficient, qc, and the single-granule reentrainment coefficient, qR, contain the functional relationships with respect to particle size, gas velocity, and other factors including temperture. The predicted trends of particle collection at temperatures different from ambient can be estimated by inspection of the temperature-dependent terms in the single-granule collection coefficients for impaction, diffusion, and sedimentation. In general, high temperature is expected to reduce the collection efficiency for particles larger than a few tenths of a micron in diameter. Adhesion and drag forces that affect particle reentrainment also change at elevated temperatures. For example, capillary force will decrease at high temperatures,
Table I. Experimental Conditions block I
block I1
block I11
run no.
Ka
VG
Vgc
run no.
Ka
VG
Vgc
run no.
Ka
VG
18 17 16 20 15 19
1.3 3.7 1.3 3.7 2.5 2.5
0.026 0.026 0.049 0.049 0.037 0.037
26 1 139 139 26 1 200 200
13 12 9 11 14 10
1.3 3.7 1.3 3.7 2.5 2.5
0.026 0.026 0.049 0.049 0.037 0.037
139 261 261 139 200 200
4 6 3 7 2 1 5 8
0.5 4.5 2.5 2.5 2.5 2.5 2.5 2.5
0.037 0.037 0.019 0.056 0.037 0.037 0.037 0.037
a K = intergranular dust deposit ratio ( % by weight). VG = granule velocity (mmis). (mmis) (bed depth = 1 3 0 mm and granule diameter = 2.1 mm for all runs).
and air drag will increase for particles large than a few tenths of a micron in diameter. However, ash particles may become sticky and thereby reduce reentrainment. The proposed single-granule coefficients should be useful to correlate results of empirical studies to characterize selected dust-granule systems at elevated temperatures.
Experimental Section Experiments were performed to quantify the coefficients 70 and vR in eq 10 and to investigate the functional relationship of factors affecting reentrainment. The CMGBF consisted of three gas-tight sections: a granule storage bin, a 203-mm diameter bed column, and a granule control mechanism. Granules flowed by gravity downward through the column, cocurrently with the gas flow. Cleaned gas exited through a circumferential gas-exit screen located below the active filtering porition of the CMGBF. High density ( p =~ 3250 kg/m3) alumina granules with a diameter of average mass of 2.1 mm were used for all runs. All runs were at ambient temperature and pressure. The experimental apparatus is described in detail elsewhere (25). The test aerosol was electrostatically precipitated fly ash from a utility boiler fiied with pulverized coal. The fly ash was resuspended by an NBS dust feeder (26) and had a count median diameter of 0.3 pm. Samples for particle size analysis were isokinetically collected on Nuclepore filters. Photomicrographs were obtained by scanning electron microscope (SEM), and particles were sized and counted with a Zeiss MOP image analyzer. Twenty runs with the CMGBF were conducted in a “central composite design” experiment (27) with three control variables: V,, superficial gas velocity; V,, granule velocity; K, the ratio of collected dust mass to granule mass within the conditioned bed at steady state. The nominal factor levels are shown in Table I. All experiments described here were conducted at constant bed depth and granule size; effects of these factors were reported in a previous paper (13). The weight ratio, K , is an experimental surrogate for the dust solidity within the bed, spaThe relationship between these variables is sp
= (1- Eo)PGK/Pp
(14)
where sp = dust solidity (dimensionless),eo = porosity of clean bed (dimensionless), pG = granule density (kg/m3), pp = dust particle density (kg/m3),and K = ratio of dust mass collected to granule mass in the bed (kg/kg). Although dust solidity within the bed, sp, could not be measured directly, ratio K could be measured and used to calculate spthrough eq 14. A series of end-of-run penetration measurements were conducted to identify the significance of penetration
vgc
200 200 200 200 100 300 200 200
V,= superficial gas velocity
mechanisms including (A) straight-through penetration, (B) air scouring, and (C) reentrainment caused by granular motion. After the normal penetration measurements were completed, bed motion was stopped and penetration was immediately measured again. This dust-on/ bed-stopped situation measured the penetration straight through the loaded bed. Next the dust feeder was stopped and the downstream concentration was determined with the bed still motionless to measure the effect of the air scouring at the superficial gas velocity of the run. Finally the bed motion was restarted but with no dust fed. This dustoff/bed-moving situation allowed sampling of the dust initially collected but subsequently reentrained from the loaded bed as the result of granular motion. Mass penetration and pressure drop data for all runs shown in Table I are reported elsewhere (25). Penetration data by count in particle size categories between 0.08 and 7.3 pm were obtained for runs 1-9. Fractional penetration data were obtained for these nine runs for the conditions of (1)an initial clean moving bed when dust feed began, (2) a normal cocurrent steady-state bed at the end of at least two bed volume replacements, and (3) straight-through penetration of the stationary loaded bed. Particle size distributions were also obtained for these nine runs for the particles reentrained from the moving bed when dust feed had stopped. Particle size information obtained from runs in block I11 allows comparison of the effect of each control variable at its extreme and center-point conditions. Center point conditions are replicated for error determination. Average fractional penetration data for runs 1-9 are shown in Figure 2 for the moving and stationary loaded bed cases. Penetration in the submicron range was approximately the same whether the loaded bed was moving or not; however, penetration in the larger particle sizes was clearly greater when the loaded bed was moving. The relatively greater variability in the penetration data for the normal moving bed is due to the influence of control variables, other than particle size, not separated in this crude average but discussed below. Straight through penetration was influenced much less by these factors, as indicated by reduced variability in the lower curve in Figure 2. Particle size data from the photomicrographs clearly showed that the reentrained particles were larger than the particles penetrating straight through the stationry loaded bed. Very small particles (approximatelyless than 0.3 pm) were not found on the photomicrographs of reentrained particles, suggesting that small particles were not reentrained. Although agglomerates were present in the reentrained particles as observed on SEM photomicrographs, the proportion of agglomerates in any size category was not significantly different from the proportion of agglomerates Environ. Sci. Technol., Vol. 17, No. 1, 1983 23
25 --
8 Normal Penetration 2 2 S.E.
T
Bed Moving
.L
,$ Straight Through Penetration 2 2S.E. Bed S m p e d
20 --
T
A
E C
.-0
5 154-
C
T
? ;
2
\
lo--
f/ A 5 --
I
Figure 2. Average penetration VI.
particle size for runs 1-9.
in the same size category either upstream of the CMGBF or in the particles penetrating straight through. The fly ash was well combusted and consisted of glassy spheres, which normally do not agglomerate appreciably. Thus, it appears that most particles penetrated or were reentrained without significant additional agglomeration. Evaluation of Single Granule Reentrainment Coefficient Reentrainment due to granular motion is exemplified by the difference between penetration when the bed is operating normally and straight-through penetration immediately after the bed is stopped. The increased penetration due to reentrainment in larger particle sizes can be seen in Figure 2. These fractional penetration data were used to quantify the reentrainment coefficient in the CMGBF penetration model. Equation 10 with 7]R = 0 was used to calculate the single dirty-granule collection coefficient, vG, from the straight through penetration data in different particle size categories. The empirical collection coefficient, qG, calculated in this fashion may contain the effects of simple air scouring, bounce, and reentrainment of particles unrelated to granular motion. On an overall mass penetration basis, simple air scouring of particles from the loaded, stationary bed was negligible. The effective porosity of the bed 6 , accounting for the intergranular dust deposit, was estimated from eq 13. For alumina granules, PbG was found to be 1950 kg/m3 by Happel's slow inversion technique (28). Loose bulk density of the fly ash, Pbp, was similarly measured as 900 kg/m3. With values of vG, c, and bed geometry, the singlegranule reentrainment coefficient, vR, was obtained from the CMGBF penetration model, eq 10, by using penetration data for the bed under normal operating conditions. Calculated values of vR for the nine runs with alumina granules are presented in Table 11. Calculated values of m range approximatelyfrom 0 to lo-'. For this calculation, a negative value of m occurs when the penetration straight 24
Envlron. Sci. Technol., Vol. 17, No. 1, 1983
Table 11. Calculated Single-Granule Reentrainment Coefficient, V R (Listed Values Are 7)R x particle diameter, pm (midpoint) run no.
0.080.23 (0.16)
0.230.46 (0.35)
1 2 3 4 5 6 7 8 9 av SE
1.31 9.61 14.9 5.61 2.15 47.3 49.1 22.3 0.0 16.9 6.4
-13.4 -7.99 -8.01 2.47 -6.57 3.97 22.0 15.5 -3.42 0.51 3.9
0.460.91 (0.69) -2.50 -21.3 9.73 2.18 -4.56 80.9 18.6 8.73 9.71 11.3 9.5
0.911.83 (1.4) 3.64 2.63 28.7 -8.46 3.66 88.3 82.1 40.9 13.6 28.3 11.8
1.833.66 (2.7) 1.46 30.7 24.7 18.8 19.9 82.9 49.0 58.0 33.3 35.4 8.1
3.667.31 (5.5) 11.4 58.3b 91.6jb 19.5 52.7 37.9 45.8 20.7 64.0 36.0 7.4
Conditions: e o = 0.4; E = eq 3 ; PbG = 1950 kg/ms; pbp = 900 kg/m3;d G = 2.1 mm (alumina). Penetration straight through = 0, and q R was estimated but not included in averages or regression. a
through the stationary, loaded bed exceeds the penetrtion in the moving bed case. As shown in Table 11, negative values occurred for small particles where measurement errors for the two penetration measurements overlap. Table I1 shows the mean values of vR as a function of particle size, again ignoring the effect of other variables. The reentrainment coefficient increases with particle diameter and appears to approach zero for particles roughly 0.3 pm in diameter. This approach to zero reentrainment is indicated in Table I1 by calculated zero or negative values of vR in the submircon range. The anomalously high value of vR in the smallest particle size category in Table I1 suggests that particles less than 0.23 pm in diameter were reentrained, but this appears to be an artifact of the calculation procedure which assumes the difference between normal penetration and straightthrough penetration is due solely t o reentrainment.
Photomicrographs of particles reentrained from moving loaded beds, after dust feed had ceased, show a complete absence of very small particles approximately less than 0.3 pm. It is more likely that these small particles penetrate fissures or other flow paths in the moving bed under normal operating conditions and that these fissures quickly seal when bed motion ceases. Thus, actual straightthrough penetration of these very small particles may have been underestimated during the stationary bed tests. In addition to particle size, the effects on ?& of the intergranular dust deposit weight ratio, K, gas velocity, V,, and granule velocity, VG, were investigated by multiple regression. The resulting equation for prediction of ?& for moving alumina granules is
where TR = single-granule reentrainment coefficient (dimensionless), K = intergranular dust deposit weight ratio (percent by weight on granules), d = particle diameter (pm), V, = superficial gas velocity Qmm/s), VG = granule velocity (mm/s). The squared multiple correlation coefficient, R2, for eq 15, is 49%, and all coefficients except the intercept are highly significant (P< 0.01). Standarized residuals were approximately normally distributed. The most significant term in 15 with respect to percent of variance explained is the product KdP1l2,indicating a positive interaction between K and dP'l2. Equation 15 tends to underpredict ?lR at the highest K values, suggesting a stronger than linear trend with K, but the present data are insufficient to resolve a more complex form. Reentrainment increases with particle diameter but shows a trend more complex than the linear one suggested earlier by theoretical consideration of the ratio of simple air drag to adhesion forces. The second term in eq 15 indicates a parabolic function for superficial gas velocity with reentrainment first increasing with gas velocity but then decreasing at the highest gas velocity. Run 1suggests such a reduction in reentrainment at high gas velocity, which may be explained by greater removal of reentrained particles by subsequent impaction on other collectors. Finally, granule velocity is seen to have a positive effect on reentrainment in the form of an incremental increase in TR in the various particle sizes. As defined here, reentrainment depends on granule motion. For a CMGBF with circumferential screen gas outlet, factors affecting intergranule shear at the wall should also strongly affect reentrainment; for example, increases in bed depth, granular bulk density, column diameter, and fluid pressure drop should all increase reentrainment. However, variations in these factors were not examined in the present study. A previous study demonstrated increased reentrainment with increased bed depth (13) as anticipated by this analysis. Equation 15, the regression equation describing reentrainment, considers the effect of other variables perhaps more closely related to resuspension of dust freed from granules by wall shear, rather than freeing of the dust from the granules in the first place. These results show that reentrainment of collected dust strongly affects penetration in a CMGBF with a circumferential screen gas outlet as tested here. Alternate gas outlet designs such as that used by Rudnick and First (29) or one incorporating a sheath of clean granules at the gas exist zone that minimize the intergranular dust deposit and granule shear at the gas outlet should minimize reentrainment and reduce overall penetration appreciably.
Although the values of the single-granule reentrainment coefficient, qR, predicted by eq 15 are specific for the CMGBF apparatus described previously, trends with operating variables should be generalizable to other granular bed designs. Also, the penetration model, eq 10, is applicable to other CMGBF configurations and should be useful in correlating experimental results. Summary
A penetration model for aerosol filtration by a cocurrent moving bed of granules has been developed. The model incorporates straight-through penetration and reentrainment of previously collected dust due to granule motion, both mechanisms having been found to be significant in experiments. The model, an extension of classical cleangranular-bed theory, utilizes the familiar concept of a single-granule coefficient for collection and proposes a similar coefficient for reentrainment. Experiments have confirmed the ability of the cocurrent moving granular bed filter to operate in a continuous mode and to enhance submicron particle filtration by the controlled formation of an intergranular dust deposit. Reentrainment was found to be a function of particle size and other factors such as gas velocity, granule velocity, and the extent of intergranular dust deposit. The single granule reentrainment coefficient, gR, was found to depend upon the product of intergranular dust deposit and the square root of particle diameter (KdP'l2)for particle diameters between 0.16 and 5.5 Hm. Further experiments are needed to develop a predictive relationship for the single-granule reentrainment coefficient as a function of dimensionless groups in the manner of the classical single-granule collection coefficients. Trends concerning reentrainment due to granule motion identified in this work may also be useful for other practical collectors in which intergranular dust deposits preclude modeling by conventional clean bed theory. Glossary
cross-sectional bed area perpendicular to gas and granule flow, m2 particle concentration in gas stream, kg/m3 particle concentration in gas stream inlet, kg/m3 particle concentration in gas stream outlet, kg/m3 bed diameter, m mass ratio of dust in bed, % by wt mass of collected dust in the differential volume, kg number of gas parcels per second passing each granule, s-l (C0/Ci) x 100, % gas volumetric flow rate, m3/s granule volumetric flow rate, m3/s superficial gas velocity, mm/s granular velocity, mm/s granular mass flow rate, g/min bed height, m differential bed depth, m granule diameter, m particle diameter, pm solidity of dust deposit, dimensionless clean-bed porosity, fraction loaded-bed porosity, fraction particle density, kg/m3 granule density, kg/m3 loose bulk density of granules, k /m3 loose bulk density of dust, kg/m single-clean-granulecollection coefficient,dimensionless single-dirty-granulecollection coefficient, dimensionless single-dirty-granule reentrainment coefficient, dimensionless
f
Environ. Sci. Technol., Vol. 17, No. 1, 1983 25
Envlron. Sci. Technol. 1903, 17, 26-31
internal coefficient of friction, dimensionless coefficient of friction at the wall, dimensionless
P P’
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M. “The Panel Bed Filter”; Electric Power Research Institute Report No. AF-50, May 1977. (7) Wade, G.; Wigton, H.; Guillory, J.; Goldback, G.; Phillips, K. “Granular Bed Filter Development Program Final (8)
(9) (10) (11) (12)
Report”; U.S. Department of Energy Report No. FE2579-19, April 1978. Yung, S. L.; Patterson, R.; Parker, R.; Calvert, S. “Evaluation of Granular Bed Filters for High Temperature High Pressure Particulate Control”;U.S.Environmental Protection Agency Report No. 60017-79-020, Jan 1979. Gutfinger, C.; Tardos, G. I. Atmos. Environ. 1979,13,853. Payatakes, A. C. Am. Znst. Chem, Eng. J. 1974,20,899. Payatakes; A. C. In “Proceedings of the 2nd World Filtration Congress”;London, Sept 1979; p 507. Goren, S. L. Appendix B in “Granular Bed Filter Development Program, Theoretical Analysis of Granular Bed Filtration Principles and Performance Prediction”;US. Department of Energy Report No. FE-2579-18, Jan 1978; p B-1.
(13) Kalinowski, T. W.; Leith, D. Environ. Znt. 1981, 6, 379. (14) Tardos, G. I.; Abuaf, N.; Gutfinger,C. J. Air Pollut. Control Assoc. 1978, 28, 354. (15) Lee, K. W.; Gieseke, J. A. Environ. Sei. Technol. 1979,13, 466. (16) Straus, W. “Industrial Gas Cleaning”,2nd ed.; Pergamon Press: New York, 1975; p 312. (17) Corn, M. J . Air Pollut. Control Assoc. 1961, 11, 523. (18) Fuchs, N. A. “Mechanics of Aerosols”; Pergamon Press: New York, 1964. (19) Goren, S. L.; O’Neill, M. E. Chem. Eng. Sci. 1971,26, 235. (20) Taub, S. Ph.D. Thesis, Carnegie-Mellon University, Pittsburg, PA, 1970. (21) Delaplaine, J. W. Am. Znst. Chem. Eng. J. 1956, 2, 127. (22) Brandt, H. L.; Johnson, B. M.Am. Znst. Chem. Eng. J. 1963, 9, 771. (23) Grossman, G. Am. Znst. Chem. Eng. J. 1975, 21, 720. (24) Toyama, S. Powder Technol. 1970, 4, 214. (25) Kalinowski,T. W. Sc.D. Thesis, Harvard University, Boston, MA, 1981. (26) Hinds, W. In “Generation of Aerosols”;Willeke K., Ed.; Ann Arbor Science: Ann Arbor, MI, 1980. (27) Cochran, W. G.; Cox, G. M. “ExperimentalDesigns”;Wiley: New York, 1957. (28) Happel, J. Znd. Eng. Chem. 1949, 41, 1161. (29) Rudnick, S.; First, M. W. In “Proceedingsof 73rd Annual Meeting of the Air Pollution Control Association”;Montreal, June 1980.
Received for review October 27, 1981. Accepted August 20,1982. This work was supported by the National Science Foundation, Grant ENG77-26975. Alumina granules were supplied by Electrorefractoriesand Abrasives Division of Ferro Corp., East Liverpool, OH.
Factors Affecting the Soluble-Suspended Distribution of Strontium-90 and Cesium-I 37 in Dardanelle Reservoir, Arkansas David M. Chittenden I 1 Department of Chemistry, Arkansas State University, State University, Arkansas 72467
The variations of the concentrations of wSr and 137Cs at four stations in Dardanelle Reservoir were analyzed as functions of two parameters: concentration of ionic species and the activity released, A,, from the two 900-MW reactors that use the reservoir as a source of cooling water. Multiple regression analyses were performed on the radionuclide concentrations by using the two parameters as predictors. The analyses indicated that wSr is in a state of equilibrium between the solution and the suspended sediment. The position of the equilibrium was found to be quite sensitive to changes in the concentration of alkaline earth cations, M(I1). Thus, the concentration of M(I1) has a substantial effect on the removal of Y3r from the water column. The 137Csconcentration varied as A,, indicating that solution-sediment equilibrium has not been attained. Introduction
The behavior of fission-produced radionuclides in the aquatic environment has been extensively studied since the time of the first nuclear weapons tests. Of great concern lately has been the interaction of dissolved radionuclides with clay minerals. This interaction is of great importance in the study of the fate of radionuclides released 26
Envlron. Sci. Technol., Vol. 17, No. 1, 1983
from power reactors and in studies of the geological storage of nuclear wastes. These studies can be classified according to the nature of the aqueous medium: solutions of high ionic strength containing relatively large amounts of radionuclides used in laboratory studies with processed clay minerals; marine and estuarine water; fresh water from lakes and rivers. In the latter two categories, the clay minerals are constituents of suspended or bottom sediments. Laboratory studies of the distribution of 137Csand between solutions of high ionic strength and clay minerals, with an eye toward geological storage of nuclear waste, have been reviewed and described by Erickson (1) and Shiao et al. (2). It was found (2) that the distribution coefficient, D , of trace amounts of Sr(I1) between a montmorillonite, pretreated to be completely of the Ca form, and a solution of Ca(I1) could be expressed by the equation k = constant log D = -log [Ca(II)] + k (1) where [Ca(II)] was the concentration of Ca(I1) in solution. The distribution coefficient for trace Cs(1) was expressed as k’ = constant log D = -0.5 log [Ca(II)] + k’
0013-936X/83/09 17-0026$01.50/0
0 1982 American Chemical Society
